Solve -x^3 10x^2 - 27x^21

Question

Simplify the expression

- 10 x^{5} - 27 x^{2}

Evaluate

- x^{3} \times 10 x^{2} - 27 x^{2} \times 1

Multiply

More Steps

Multiply the terms

- x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

- x^{3 + 2} \times 10

Add the numbers

- x^{5} \times 10

Use the commutative property to reorder the terms

- 10 x^{5}

- 10 x^{5} - 27 x^{2} \times 1

Solution

- 10 x^{5} - 27 x^{2}

Show Solution

Factor the expression

- x^{2} (10 x^{3} + 27)

Evaluate

- x^{3} \times 10 x^{2} - 27 x^{2} \times 1

Multiply

More Steps

Multiply the terms

x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 10

Add the numbers

x^{5} \times 10

Use the commutative property to reorder the terms

10 x^{5}

- 10 x^{5} - 27 x^{2} \times 1

Multiply the terms

- 10 x^{5} - 27 x^{2}

Rewrite the expression

- x^{2} \times 10 x^{3} - x^{2} \times 27

Solution

- x^{2} (10 x^{3} + 27)

Show Solution

Find the roots

x_{1} = - \frac{3 3 100}{10}, x_{2} = 0

Alternative Form

x_{1} \approx - 1.392477, x_{2} = 0

Evaluate

- x^{3} \times 10 x^{2} - 27 x^{2} \times 1

To find the roots of the expression,set the expression equal to 0

- x^{3} \times 10 x^{2} - 27 x^{2} \times 1 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 10 x^{2}

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 10

Add the numbers

x^{5} \times 10

Use the commutative property to reorder the terms

10 x^{5}

- 10 x^{5} - 27 x^{2} \times 1 = 0

Multiply the terms

- 10 x^{5} - 27 x^{2} = 0

Factor the expression

- x^{2} (10 x^{3} + 27) = 0

Divide both sides

x^{2} (10 x^{3} + 27) = 0

Separate the equation into 2 possible cases

x^{2} = 0 10 x^{3} + 27 = 0

The only way a power can be 0 is when the base equals 0

x = 0 10 x^{3} + 27 = 0

Solve the equation

More Steps

Evaluate

10 x^{3} + 27 = 0

Move the constant to the right-hand side and change its sign

10 x^{3} = 0 - 27

Removing 0 doesn't change the value,so remove it from the expression

10 x^{3} = - 27

Divide both sides

\frac{10 x ^{3}}{10} = \frac{- 27}{10}

Divide the numbers

x^{3} = \frac{- 27}{10}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{27}{10}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{27}{10}

Calculate

x = 3 - \frac{27}{10}

Simplify the root

More Steps

Evaluate

3 - \frac{27}{10}

An odd root of a negative radicand is always a negative

- 3 \frac{27}{10}

To take a root of a fraction,take the root of the numerator and denominator separately

- \frac{3 27}{3 10}

Simplify the radical expression

- \frac{3}{3 10}

Multiply by the Conjugate

\frac{- 3 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{- 3 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

\frac{- 3 3 100}{10}

Calculate

- \frac{3 3 100}{10}

x = - \frac{3 3 100}{10}

x = 0 x = - \frac{3 3 100}{10}

Solution

x_{1} = - \frac{3 3 100}{10}, x_{2} = 0

Alternative Form

x_{1} \approx - 1.392477, x_{2} = 0

Show Solution